Description
Definitions and Mathematical Knowledge explores the philosophical foundations of mathematical definitions and their epistemic significance. Andrea Sereni investigates the relationship between how we define mathematical objects and what we can know about them, addressing fundamental questions about the nature of mathematical understanding.
The work examines competing theories of mathematical definitions, including conventionalist, essentialist, and pragmatist approaches. Sereni analyzes how definitions function in mathematical practice, their role in proof and discovery, and whether they provide genuine insight into mathematical reality or merely organize our conceptual schemes.
This Element is essential for philosophers of mathematics, mathematicians interested in foundational questions, and anyone seeking to understand how mathematical knowledge is structured and justified. The analysis bridges abstract philosophical inquiry with concrete mathematical examples, making it accessible while maintaining rigorous argumentation about the nature of mathematical understanding.
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